Symmetry‐Breaking Triplet Excited State Enhances Red Afterglow Enabling Ubiquitous Afterglow Readout

Abstract Molecular vibrations are often factors that deactivate luminescence. However, if there are molecular motion elements that enhance luminescence, it may be possible to utilize molecular movement as a design guideline to enhance luminescence. Here, the authors report a large contribution of symmetry‐breaking molecular motion that enhances red persistent room‐temperature phosphorescence (RTP) in donor‐π‐donor conjugated chromophores. The deuterated form of the donor‐π‐donor chromophore exhibits efficient red persistent RTP with a yield of 21% and a lifetime of 1.6 s. A dynamic calculation of the phosphorescence rate constant (k p) indicates that the symmetry‐breaking movement has a crucial role in selectively facilitating k p without increasing nonradiative transition from the lowest triplet excited state. Molecules exhibiting efficient red persistent RTP enable long‐wavelength excitation, indicating the suitability of observing afterglow readout in a bright indoor environment with a white‐light‐emitting diode flashlight, greatly expanding the range of anti‐counterfeiting applications that use afterglow.


Introduction
Persistent (lifetime >100 ms) room-temperature (RT) emission harvesting from metal-free, heavy-atom-free organic chromophores is an active area of research due to diverse imaging advancements. [1]This is especially important for bioimaging [2] and anti-counterfeit applications [3] as it helps to avoid interference from background autofluorescence.1e,2c,e,3a] However, persistent RT emission yield is low in red wavelengths. [4]Persistent RT phosphorescence (RTP) from simple (metal-and heavy-atom-free) organic chromophores enables persistent bright emission compared with long persistent emission via charge separation and DOI: 10.1002/advs.2023088971b,f,5] Accordingly, persistent RTP from simple organic chromophores might increase the resolution of imaging and minimize autofluorescence challenges. [6]4h] Nevertheless, nearly 100% nonpersistent emission yield at red wavelengths of fluorescent chromophores and metal complexes has been reported. [7]Therefore, why simple organic chromophores with highly efficient red persistent RTP have not been reported to date remains unclear.Commonly, to increase the RTP yield, the rate constant of radiation from T 1 (k p ) should be large compared with the rate constant of the nonradiative transition from T 1 (k nr ) at RT. [8] However, k nr (RT) increases in a manner that is approximately proportional to the square of the wavelength based on the energy gap law, and k p is inversely proportional to the cube of the wavelength. [8]Therefore, k p > k nr (RT) is challenging for persistent RTP at long wavelengths (red and near-infrared).Therefore, discovering key elements of molecular structures and geometries that can selectively enhance k p without increasing k nr (RT) is crucial for enhancing the efficiency of persistent RTP at long wavelengths.
Here we report a substantial contribution of thermally induced symmetry-breaking of symmetric conjugated chromophores to enhancing k p without enhancing k nr (RT), in a manner that achieved red persistent RTP with a yield of >20%.To evaluate chromophores that exhibit more efficient red afterglow RTP, we selected dibenzo [g,p]chrysene (DBC) as a phosphorescent conjugated unit () and phenoxazine as a planer donating substituted unit (D).Common quantum chemical calculation of k p by using T 1 -optimized structures suggests that the RTP yield of the D--D structure is small compared with the D- structure.However, the optically determined k p of the D--D structure is larger than that of D-, although the two structures have comparable k nr (RT).A proposed dynamic quantum chemical calculation-considering the dihedral angle between the D and  units, depending on the thermal energy-Figures out that symmetry-breaking caused by independent changes of two dihedral angles in the D--D structure largely enhanced k p without increasing k nr (RT).Because of the large selective enhancement of k p by the symmetry-breaking, a deuterated compound of the D--D structure indicates red afterglow RTP with a RTP yield of 21% and an RTP lifetime of 1.6 s.We applied films using the high-efficiency red persistent RTP chromophore to visually observe afterglow in the dark by ) Schematic that shows the calculation zone regarding the relationship between the excitation energy and molecular coordinates for predicting k nr (RT).c) Predicted results of k nr (RT) using the procedure in (b) for 1h-3h.Black-filled circles represent previously reported data for other chromophores; reported in references, [3e,4g-i,6] and. [10]The Black dashed line represents a supporting line with a slope of 1. d) Schematic that shows the calculation zone regarding the relationship between the excitation energy and molecular coordinates for predicting k p .e) Predicted result of k p using the procedure in (d) for 1h-3h.f) Visualization of predicted results regarding k p and k nr (RT).
simply turning off the common room light, and in bright environments by simply illuminating a white-light-emitting diode (LED) on a portable phone.This enables ubiquitous afterglow anti-counterfeiting technology that does not require strong ultraviolet (UV) or deep blue light sources.

Prediction of k nr (RT) and k p by Using a Previously Reported Method
1c,4a,h] Three kinds of DBC derivatives [chromophores 1h-3 h (Figure 1a)] are the focus of our work.For the three chromophores, we calculated the change of k p and k nr (RT) using previously reported quantum chemical calculation procedures to predict the order of the persistent RTP yield.3e,4g-i,6,8,10] Analysis using the reported vibrational SOC analysis suggests that k nr (RT) of 1h-3 h are comparable and located in the range of 1×10°to 2×10°s −1 (Figure 1c).Regarding k p , the nth-order singlet excited state (S n ) is substantially related to k p , and k p is substantially related to the transition dipole moment between S n and S 0 ( S n −S 0 ) and the SOC between S n and T 1 (⟨S n | ĤSO |T 1 ⟩). [6,11]3e,4g-i,6,11] The calculation of k p using the optimized T 1 geometry predicts the relationship 1 h < 3 h < 2 h for the value of k p (Figure 1e).Therefore, the predictions of k nr (RT) and k p suggest that the red RTP yield of the three chromophores has a relationship 1 h < 3 h < 2 h when the intersystem crossing yield from the lowest singlet excited state (S 1 ) to the triplet states (Φ isc ) is comparable for the three chromophores (Figure 1f).

Optically Determined k nr (RT) and k p
Contrary to the prediction in Figure 1, the RTP yield of 3 h was larger than that of 2 h.We prepared chromophores 1h-3 h and 3d (Figure 2a) (Section S1 and S2, Supporting Information) and analyzed them by 1 H nuclear magnetic resonance (NMR), 13 C NMR, high-resolution mass spectrometry, and elemental analysis (Section S3 and Figures S1-S17, Supporting Information).Chromophores 1h-3 h and 3d have absorption wavelengths <460 nm when dispersed in amorphous -estradiol at a concentration of 0.3 mass fraction (Figure 2b).Chromophores 1h-3 h and 3d dispersed in amorphous -estradiol exhibit fluorescence peaks at 397, 469, 494, and 491 nm, respectively (Figure S18, Supporting Information).The additional emission peak at 600-650 nm under excitation at 340 nm is due to the phosphorescence band (Figure 2c, top).Chromophore 3 h exhibits stronger emission from 600-650 nm compared with 1 h and 2 h, and the emission intensity of 3d from 600-650 nm is increased compared with that of 3 h.After ceasing excitation, the red emission with a spectral peak from 600 to 650 nm remained (bottom of Figure 2c).The afterglow emission was caused by persistent RTP because the emission decay had single-exponential characteristics (Figure 2d).The RTP peak wavelength of 1 h, 2 h, 3 h, and 3d in amorphous -estradiol was 624, 626, 625, and 625 nm, respectively; in which radiation with wavelength >600 nm is commonly considered as red emission.The phosphorescence lifetime ( p ) at RT of 0.3 wt.% 1h-3 h and 3d dispersed in amorphous -estradiol was 0.58, 0.61, 0.64, and 1.6 s, respectively.The steady-state RT emission yield (Φ e ) at RT of 0.3 wt.% 1h-3 h and 3d dispersed in amorphous -estradiol was 23%, 21%, 32%, and 49%, respectively.By comparing the spectral intensity of the steady-state RT emission with that of the persistent RTP soon after ceasing excitation, the phosphorescence yield (Φ p ) at RT of 0.3 wt.% 1h-3 h and 3d dispersed in amorphous -estradiol was determined as 2.9%, 6.6%, 8.7%, and 21%, respectively (Figure 2a; Figure S19, Supporting Information).The fluorescence yield (Φ f ) at RT of 0.3 wt.% 1h-3 h and 3d in dispersed in amorphous -estradiol was determined as 19%, 14%, 24%, and 28% by substituting Φ p (RT) from Φ e (RT).The value of Φ p (RT) = 21% for 3d is the largest among previously reported red afterglow RTP-emitting materials with an RTP peak wavelength >600 nm and an average delayed emission lifetime of >100 ms. [12]In delayed fluorescence materials, Table 1.Summary of photophysical parameters related to singlet states of chromophores (0.3 wt.%) doped into amorphous -estradiol.the delayed emission substantially decreases from 1-100 ms after ceasing excitation, even when afterglow emission is observed (Figure S20, Supporting Information).This causes a large decrease in the average delayed emission lifetime, and the utilization of photons generated after 100 ms substantially decreases.However, the delayed emission from intrinsic RTP emission negligibly decreased from 1 to 100 ms after ceasing excitation.This is suitable for obtaining brighter afterglow harvesting-without interference from autofluorescence-by using a portable chargecoupled device camera with a slow data collection time (>20 ms) and small-scale capabilities.The temperature dependence of Φ f and Φ p indicates that Φ f and Φ p negligibly decreased from 77 K to RT (Figure 2e; Figure S21, Supporting Information). p (T) of the chromophores did not substantially decrease from 77 K to RT (top in Figure 2f; Figure S22, Supporting Information).

Comparison Between Optically Determined Results and Previously Reported Calculation Results for k nr (RT) and k p
The optically determined relationship between k nr (RT) and k p had a different tendency compared with the predicted relationship between k nr (RT) and k p in Figure 1.The experimentally determined k nr (RT) and k p , Φ isc of 0.3 wt.% 1h-3 h and 3d in amorphous -estradiol are shown in Tables 1 and 2. The Φ isc values calculated using 1 − Φ f (RT) were ≈80%, 86%, 77%, and 72% for 1h-3 h and 3d, respectively (Table 1).The approximation of Φ isc ≃ 1 − Φ f (RT) is reasonable for the chromophores.This is because the value of Φ isc in amorphous -estradiol is comparable to that in benzene (Figures S23-S25 and Table S2, Supporting Information) [13] and the fluorescence spectra (Figure 2b; Figure S26b, Supporting Information), as well as the fluorescence lifetime (Figures S18 and S26c, Supporting Information) did not substantially change between benzene and -estradiol.By substituting Φ p (RT),  p (RT), and Φ isc into the common formula Φ p (RT) = Φ isc k p  p (RT), k p of 1h-3 h, and 3d dispersed in amorphous estradiol was determined as 0.063, 0.13, 0.18, and 0.18 s −1 , respectively (Table 2).We obtained the temperature dependence of k nr (T) + k q (T) by applying Φ p (T), k p , and 2F, bottom).Assuming that k nr (T) and k q (T) have an exponential function as 1/T (Figure S27, Supporting Information), we separated k nr (T) and k q (T) to determine k nr (RT) and k q (RT) (Table 2). [10]The temperature dependence of the emission properties of thin films doped with 0.3 wt.% 3d in other representative nonconjugated polymer hosts was also verified.However, Φ p (RT) in these polymers is smaller than that in -estradiol (Section S7, Figure S28, Tables S4 and  S5, Supporting Information).In these polymers, unlike amorphous -estradiol, more pronounced multiexponential phosphorescence decay characteristics, which indicate poor dispersion of latent dyes, were also confirmed (Section S7, Figures S29-S31, Supporting Information).Such differences in the degree of aggregation impart difficulties in quantitatively comparing k nr and k p for each guest chromophore.Therefore, in this paper, data in amorphous -estradiol were used to discuss the relationship between k nr , k p , and the molecular structure of the guest chromophore.
The optically measured k nr (RT) of 1h-3 h in amorphous estradiol was comparable and in the range of 1×10°to 2×10°s −1 .1c,6] The determined values of k nr (RT) of 1h-3 h closely corresponded to a previously determined correlation line between the optically determined k nr (RT) and calculated k nr (RT) values, considering all vibrations allowed at RT (Figures S32-S34, Tables S6 and S7,    Supporting Information).Therefore, the prediction of k nr (RT) in Figure 1c worked well for 1h-3 h.However, the previously reported static k p prediction by using optimized T 1 geometries did not work for 1h-3 h.When we considered the experimental result and the predicted result regarding k p , calculated based on the fixed T 1 geometry (k p T 1 opt ) (Figure 3a-(i),(ii)) for 1h-3 h, the relationship between the optically observed k p and the calculated k p T 1 opt of 3 h did not have a strong correlation (Figure 3a-(iii)).In addition, analysis after adding a D--D structure with a different chemical backbone from DBC exhibited a deteriorated correlation for the k p versus k p T 1 opt plot (Figure S35a, Supporting Information).This indicates that previously reported static k p calculations based on a fixed T 1 geometry cannot be universally used to predict k p of conjugated structures.Upon focusing the data of 1 h and 2 h in k p versus k p T 1 opt plots (Figure 3a-(iii)), the data of 1 h and 2 h are close in a manner that results in a supporting correlation line with a slope of 1; whereas the data of 3 h were somewhat far from the line.Therefore, we potentially underestimated the calculated k p T 1 opt of 3 h.

Role of Symmetry-Breaking in Selectively Enhancing k p Compared with k nr (RT)
The reason for the potential underestimation of the k p of 3 h is related to the symmetric structure of 3 h.Here, the thermal distribution depending on the dihedral angle between phenoxazine and the DBC unit ( 1 for 2 h, and  1 and  2 for 3 h) is considered (Figure 3b-(i).We performed a dynamic calculation of k p by considering the independent change of  1 and  2 , based on the thermal energy (k p  ) (Figure 3b-(ii)).The result exhibited a much better correlation between the optically measured k p and the pre-dicted result (k p  ), based on the proposed dynamic calculation (Figure 3b-(iii)).In addition, analysis after adding a D--D structure with a different chemical backbone from DBC exhibited a good correlation for the k p versus k p  plot (Figure S35b, Supporting Information).To perform the calculation shown in Figure 3b for 3 h, we initially determined the T 1 -optimized geometry. 1 and  2 of the optimized T 1 geometry were ≈70°.Next, we calculated the energy increase compared with the optimized T 1 geometry (ΔE) (Figure 3b (ii)) upon changing  1 yet fixing  2 = 70°(Figure 4a-(i)).By using the ΔE, we calculated the possibility of each distorted geometry at RT [p(RT)], depending on the change of  1 , by using p(RT) ( 1 ) = exp(−ΔE( 1 )∕kT)∕ ∫ exp(−ΔE( 1 )∕kT)d 1 based on the Boltzmann distribution (Figure 4a (ii)), where k is the Boltzmann constant.Upon changing  1 from 70°, p(RT) decreased.For the various geometries, we performed the calculation of k p (Figure 4a-(iii)).As a crucial point, k p had the smallest value when  1 =  2 = 70°(arrow in Figure 4a-(iii)).Then, we calculated ΔE, p(RT), and k p in the same manner as upon changing  1 yet fixing  2 = 60°(Figure 4b).Similarly, we observed the smallest value of k p when  1 =  2 = 60°(arrow in Figure 4b-(iii)).Thus, the origin of small k p for symmetric D--D structures in which  1 =  2 needs to be understood.
To elaborate on this point, we constructed a 2D histogram of k p regarding independent changes of  1 and  2 (Figure 4c) [k p ( 1 ,  2 )] (Figure 4d).Because there was a large decrease in k p values for  1 =  2 , a symmetry-forbidden line regarding k p was evident.This indicates a mechanism for the observation that symmetric structures of 3 h corresponded to substantially decreased k p .We also calculated the dependence of ΔE on independent changes of  1 and  2 [ΔE( 1 ,  2 )] (Figure 4e).By using ΔE( 1 ,  2 ), we calculated p(RT) (depending on independent changes of  1 and  2 [p(RT)( 1 ,  2 )]) by using p(RT) ( 1 ,  2 ) = exp(−ΔE( 1 ,  2 )∕kT)∕ ∬ exp(−ΔE( 1 ,  2 )∕kT)d 1 d 2 based on the Boltzmann distribution (Figure 4f).Finally, we calculated a 2D histogram of p(RT)( 1 ,  2 )k p ( 1 ,  2 ) from data in Figure 4e-g).Integration of p(RT)( 1 ,  2 )k p ( 1 ,  2 ) regarding  1 and  2 was by the average value of k p (k p  ) when  1 and  2 were distributed based on the Boltzmann theory.We calculated the k p  value of 3 h to be 0.18 s −1 .Regarding 2 h, we considered the change of  1 and determined k p  to be 0.073 s −1 (Figure S36, Supporting Information).As a result, we observed a good correlation between the optically determined k p and the calculated k p  based on dynamic calculation for 1h-3 h (Figure 3b-(iii)).Therefore, 2 h and 3 h have a distribution of  1 and  2 even upon dispersal into a solid host.The static calculations that do not consider the coordinate change based on the thermal distribution resulted in three times smaller k p T 1 opt (0.062 s −1 ) based on fixed T 1 geometry compared with k p  (0.18 s −1 ) of 3 h chromophore.However, the changes in the dihedral angles ( 1 and  2 ) were negligibly related to k nr (RT) (Section S8 and Figure S37, Supporting Information).

Origin of Enhancing k p by Symmetry-Breaking
Although the contribution of symmetry-breaking by changing  1 and  2 to enhanced k p is clear, further detailed analysis regarding parameters contained in k p indicates that an increase of the S n -S 0 transition dipole moment by changing  1 and  2 enhanced k p .For some chromophores in previous re-ports, k p is approximately calculated based on the following formula, [6,11] where E T 1 −S 0 is the energy difference between T 1 and S 0 ,  S n −S 0 is the transition dipole moment between S n and S 0 , ⟨S n | ĤSO |T 1 ⟩ is the SOC between S n and T 1 , and E S n −T 1 is the energy difference between S n and T 1 .The calculated values of E T 1 −S 0 in 1h-3 h are comparable (Figure S38, Supporting Information) and reasonably explain the red energy of the chromophores, upon considering a statistical relationship between the optically determined E T 1 −S 0 values and the calculated E T 1 −S 0 (Figure S39, Supporting Information).Because of the comparable E T 1 −S 0 among 1h-3 h, the difference of k p could correspond to a different  S n −S 0  n based on Equation (1).On the basis of Equations ( 1) and ( 2), k p is approximately proportional to  S n −S 0 2 and ⟨S n | ĤSO |T 1 ⟩ 2 (Figure 5a).
Therefore, visualization of  S n −S 0 2 and ⟨S n | ĤSO |T 1 ⟩ 2 for each n (Figure 5b) is useful for understanding the main contribution to the selective enhancement of k p .For the symmetric optimized T 1 geometry of 3 h ( 1 = 70°,  2 = 70°),  S n −S 0 2  n 2 in n = 1 and n = 2 mainly contributed to k p ; whereas  S n −S 0 2  n 2 in n = 2 exhibited a lesser contribution (Figure 5b-(i)).In S 2 , the small  S 2 −S 0 2 (Figure 5b-(iii)) corresponded to the small  S 2 −S 0 2  2 2 , al- though ⟨S 2 | ĤSO |T 1 ⟩ 2 was large (Figure 5b-(ii)).Therefore, the small  S 2 −S 0 2 is a reason for the underestimated k p T 1 opt (0.063 s −1 ) for the symmetric optimized T 1 structure of 3 h.However, there was also a disrupted symmetric geometry with  1 = 70°and  2 = 80°, depending on the thermal distribution at RT (Figure 4f).Regarding the thermally activated broken symmetric geometry in which  1 = 70°and  2 = 80°,  S 2 −S 0 2 substantially increased (Figure 5b-(vi)); whereas ⟨S 2 | ĤSO |T 1 ⟩ 2 did not substantially decrease (Figure 5b-(v)).Because  S 2 −S 0 2  2 2 of the disrupted symmetric geometry substantially increased compared with the symmetric geometry in which  1 =  2 = 70°(Figure 5b-(iv)), the increase of  S 2 −S 0 2 contributed to the enhanced k p .The large enhancement of  S 2 −S 0 2 by symmetry-breaking can be understood by considering the symmetry-forbidden transition dipole moment in the S 2 -S 0 transition.We defined two molecular orbitals primarily relating to the S 2 -S 0 transition as  a and  b .Regarding the symmetric geometry with  1 =  2 = 70°, the overlapping density between  a and  b ( a  b ) becomes an even function along the x-axis (Figure 6a-(i)).Therefore,  a x b becomes an odd function along the x-axis (Figure 6a-(ii)); hence ∫ a x b dx approaches 0 (Figure 6a-(iii)).Therefore,  S 2 −S 0 ∝ |∫ a x b dx| 2 becomes small and negligibly contributes to the enhancement of k p (Figure 6a-(iv)).However, the even functional characteristics along the x-axis of  a  b are slightly disrupted for the thermally activated asymmetric geometry in which  1 = 70°and  2 = 80°(Figure 6b-(i),(ii)).Therefore, a much larger value remains for ∫ a x b dx (Figure 6b-(iii)) for the symmetrybreaking geometry compared with the optimized symmetric geometry in which  1 =  2 = 70°at T 1 .The large enhancement of  S 2 −S 0 2 is because of the enhanced ∫ a x b dx that facilitates k p (Figure 6b-(iv)).When  2 approaches 90°upon fixing  1 = 70°, a phenoxazine unit becomes perpendicular to the DBC unit.Therefore,  S 2 −S 0 2 may receive a negative contribution to decrease the value when electron transfer between phenoxazine unit and DBC unit is related to  S 2 −S 0 2 .However, the contribution of breaking the symmetry-forbidden transition to enhance  S 2 −S 0 2 is still substantial.Therefore, k p of the geometry in which  1 = 70°and  2 = 90°is still large compared with that of the T 1 -optimized geometry in which  1 =  2 = 70°(Figure 4a-(iii)).We report the same mechanism of the selective k p enhancement for a different symmetry-disrupted geometry in which  1 = 70°and  2 = 50°.We observed an enhancement of  S 2 −S 0 2 and a negligible decrease of ⟨S 2 | ĤSO |T 1 ⟩ 2 for the geometry (Figure S40a, Supporting Information).The enhancement of  S 2 −S 0 2 could be explained by breaking the symmetry-forbidden transition nature as well (Figure S40b, Supporting Information).

Universality of Symmetry-Breaking Phosphorescence Enhancement in a Variety of D-𝝅-D Structures
The selective increase of k p caused by the symmetry-broken molecular structure is not exclusive to the 3 h chromophore but also applies to other D--D structures.For example, 4 h (Figure 7a, in which a DBC core is changed into a biphenyl core from 3 h) exhibited a small value of k p (7.0×10 −3 s −1 ) when calculated based on a fixed optimized geometry at T 1 .In the T 1 geometry, 4 h has a symmetric structure, and  1 as well as  2 of 4 h are ≈60°.However, the optically observed k p was 0.61 s −1 (Figure S41, Supporting Information).This is ≈100× larger than that calculated by using the fixed T 1 geometry.However, upon considering an independent distribution of  1 and  2 based on the Boltzmann distribution, the calculated k p  was 0.95 s −1 (Figure S42, Supporting Information).This is close to the optically observed k p .Because the calculated k p  of the D--D structure 4 h (0.95 s −1 ) is larger than that of D- structure (0.30 s −1 ) (Figure S43, Supporting Information), D--D structures are more suitable for enhancing k p .In the fixed geometry optimized at T 1 of 4 h ( 1 =  2 ), the S 2 -S 0 transition becomes symmetry-forbidden and does not contribute to the enhancement of k p (Figures S44a  and S44c, Supporting Information).However, for a thermally activated asymmetric geometry at RT of 4 h ( 1 ≠  2 ), the disrupted symmetry-forbidden S 2 -S 0 transition can enhance k p (Figures S44b and S44d, Supporting Information).Regarding 5 h in which the two phenoxazine donating units of 4 h change into two acridine donating units (Figure 7a), we also calculated the symmetric structure along the x-axis at the T 1 geometry.The k p was calculated by using the optimized symmetric T 1 geometry in which  1 =  2 was small (Figure S45a, Supporting Information) whereas the calculated k p increased upon disrupting the symmetric geometry ( 1 ≠ 2 ) (Figure S45b, Supporting Information).Hence, the symmetry-breaking induced selective enhancement of the k p phenomenon proved to be universal for various D--D structures composed of planer D substituents and a  unit (Figure 7b).Regarding D- structures, the symmetry-forbidden transition was not evident.Therefore, there might not be a substantial underestimation of k p for D- structures even upon using the optimized T 1 geometry for predicting k p (Figure 7c-(i)).However, because there are symmetry-forbidden transition characteristics for the S n -S 0 transition of D--D structures, static calculations that use the symmetry-optimized T 1 structure cause the substantial underestimation of k p (Figure 7c-(ii)), also resulting in under-prediction of k p compared with the corresponding result for the D- structure.The dynamic calculation that considered the statistic distribution of  1 and  2 , based on thermal energy, appropriately considered the disrupted symmetry-forbidden transition dipoles between the S n and S 0 transition (Figure 7d-(ii)).This leads to an appropriate prediction that k p of the D--D structures is larger than the k p of the D- structures.

Ubiquitous Afterglow Readout
The afterglow readout of pure organic materials requires excitation with strong UV or deep blue light.However, UV light or blue light is not always readily available.Developing a pure organic material that enables one to easily check afterglow information (by using common fluorescent tube lights or white LEDs in a mobile phone) will enable ubiquitous checking of afterglow information, i.e., ubiquitous afterglow readout.For example, when weak indoor light or sunlight acts as excitation light and the afterglow information from the medium can be determined visually in the dark with the area around the medium obscured with a hand, it is possible to obtain the afterglow information without a light source (Figure 8a).Upon termination of the strong afterglow that is evident even under indoor light is produced after the white light emitted from the LED of a common mobile phone, there is no need to create darkness; afterglow information can be more easily confirmed without a special excitation light source or photodetector because there is no need to create darkness (Figure 8b).Unlike charge-recombination-type afterglow, which remains for a long time, organic persistent RTP can produce brighter afterglow by using a weak excitation light source. [6]herefore, there is the potential for clear afterglow recognition in a bright environment upon white LED excitation.To confirm these ubiquitous afterglow readouts, we compared 3d-doped and 6d-doped amorphous -estradiol (samples 1 and 2, respectively) as films exhibiting red persistent RTP with comparable RTP lifetimes (Figure 8c). [14]Because samples 1 and 2 exhibit absorption <480 nm, they absorb light from 420-480 nm in common room light (Figure 8d).We created samples 1 and 2 exhibiting a starshaped persistent RTP pattern by photobleaching, and stacked samples 1 and 2 for evaluation (Figure 8e).Immediately upon termination of the UV light source excitation, because the excitation is sufficient the star-shaped marks from samples 1 and 2 can be easily seen in the dark environment in the stacked sample (Figure 8f-(i); Movie S1, Supporting Information).However, we observed star-shaped red afterglow with unaided eyes only from sample 1 of the staked sample in a dark environment immediately upon termination of the white room light irradiation (Figure 8f-(ii); Movie S2, Supporting Information).This is because the excitation by using room light is not large and the Φ p (RT) of sample 2 (≈2%) is much smaller than that of sample 1 (21%). [14]Furthermore, because light from 420-480 nm is included in portable LEDs when we brought the LED close to the medium and turned off the LED, we observed a red afterglow with unaided eyes under the room light environment only from sample 1 of the stacked sample (Figure 8f-(iii); Movie S3, Supporting Information).Therefore, a large Φ p (RT) at a long wavelength is crucial to extract ubiquitous afterglow readout.The ubiquitous afterglow readout, which is available under all normal circumstances, enables verification of high-performance anticounterfeit functionality without any special additional tools.

Conclusion
Although researchers commonly obtain information regarding molecular conformations that include  from single-crystal structures, information on the conformation that includes dihedral angles beyond orientation in amorphous solid media is difficult to obtain.Our results indicate that the proposed statistical analysis regarding the correlation between the experimentally observed k p and dynamically calculated k p , considering the thermal distribution of , is useful for obtaining the distribution of the dihedral angle, including symmetry information of the chromophores.Because the dihedral angle of chromophores doped into amorphous semiconductor hosts is also an active area of research (in the context of efficient and rapid thermally activated delayed fluorescence of chromophores in organic light-emitting diodes), [15] the proposed analysis is crucial for chromophores in optoelectronics applications.In addition, many D--D structures are used to enhance the S 1 -S 0 transition dipole for highly efficient fluorescent emitters used in organic lasing [16] and efficient two-photon absorption (TPA) chromophores. [17]owever, the control of S n -S 0 transition dipole has not been considered because the S n -S 0 transition dipole is not related to fluorescence and TPA.Our proposed dynamic calculation

Figure 1 .
Figure1.Prediction of red persistent RTP capability of 1h-3h chromophores based on previously reported calculations of k p and k nr (RT).a) Chemical structures.b) Schematic that shows the calculation zone regarding the relationship between the excitation energy and molecular coordinates for predicting k nr (RT).c) Predicted results of k nr (RT) using the procedure in (b) for 1h-3h.Black-filled circles represent previously reported data for other chromophores; reported in references,[3e,4g-i,6]  and.[10]The Black dashed line represents a supporting line with a slope of 1. d) Schematic that shows the calculation zone regarding the relationship between the excitation energy and molecular coordinates for predicting k p .e) Predicted result of k p using the procedure in (d) for 1h-3h.f) Visualization of predicted results regarding k p and k nr (RT).

Figure 2 .
Figure 2. Optical properties of 0.3 wt.% chromophore-doped amorphous -estradiol film.a) Chemical structures of 1h, 2h, 3h, and 3d; and condition of chromophores to generate RTP and photographs of steady-state RT emission as well as persistent RTP soon after ceasing ultraviolet excitation.b) Absorption spectra.c) Steady-state RT emission spectra (top) and persistent RTP spectra (bottom).d) RTP emission decay characteristics.e) Temperature dependence of Φ f (top) and Φ p (bottom).f) Temperature dependence of  p (top) and k nr + k q (bottom).
wavelength of fluorescence; b) Value determined with k f = Φ f (RT)/ f (RT); c) Value determined based on Φ isc = 1 − Φ f (RT); d) Value determined by using transient absorption procedure in benzene; e) Value determined with k isc = Φ isc / f (RT).
f) Values determined by using fitting lines of k nr (T) in FigureS27(Supporting Information); g) Values determined by subtracting k nr (RT), determined by using the fitting lines of k nr (T) in FigureS27(Supporting Information), from experimentally observed k nr (T) + k q (T); h) Calculated values by using the PBE0 functional and TZP basis sets, by using the optimized structure at T 1 by DFT (Gaussian09/B3LYP/6-31G(d)); i) FigureS36(Supporting Information) shows the information for calculations; j) Figure4shows the information for calculations; k) This factor is proportional to k nr (RT).Figures S32-S34 and TablesS6 and S7(Supporting Information) show the information for calculations.

Figure 3 .
Figure 3.Comparison of results regarding the prediction of k p between two procedures.a) Static k p calculation: Case by using calculation procedure based on a fixed T 1 geometry.b) Dynamic k p calculation: Case by using calculation procedure considering the change  1 and/or  2 , depending on the thermal energy.(i) Molecular condition of 2h and 3h for calculations.(ii) Schematics showing a zone that we used to calculate k p in a Jablonski diagram.(iii) Result of the relationship between the optically measured result and the calculated result.In (iii), the dashed line represents a supporting line with a slope of 1.

Figure 5 .
Figure 5. Identification of the primary contributing factor for enhanced k p in 3h in terms of the transition dipole moment as well as SOC.a) Energy diagram to explain the relationship among k p ,  S n −S 0 2 , and⟨S n | ĤSO |T 1 ⟩ 2 .b) Relationship among n,  S n −S 0 2  n 2 (i), ⟨S n | ĤSO |T 1 ⟩ 2 (ii), and  S n −S 0 2 (iii) of a symmetric geometry in which  1 = 70°and  2 = 70°(left) and a disrupted symmetric geometry in which  1 = 70°and  2 = 80°(right).

Figure 6 .
Figure 6.Visualization of breaking symmetry-forbidden transition contributing to selective k p enhancement in 3h.a,b) Schematic of molecular orbitals for k p enhancement attributable to the S 2 -S 0 transitions for a symmetric geometry in which  1 =  2 = 70°and a disrupted symmetric geometry in which  1 = 70°and  2 = 80°.

Figure 7 .
Figure 7. Role of thermally activated symmetry-breaking that facilitates a triplet radiation rate in a variety of D--D structures.a) Other examples of D--D structures that exhibit the enhancement of triplet radiation by symmetry-breaking.b) Examples of donors and  backbones that enable enhancement of triplet radiation by symmetry-breaking.c) Difference between the calculated k p in the context of D- and D--D structures upon static condition using the optimized T 1 geometry.d) Difference between the calculated k p in the context of D- and D--D structures upon dynamic condition considering the thermal distribution of the dihedral angle between the donor and  backbone.

Figure 8 .
Figure 8. Demonstration of ubiquitous afterglow readout.a) White room light-activated afterglow readout with unaided eyes in the dark as a ubiquitous afterglow readout.b) White LED-activated bright afterglow readout with unaided eyes in white room light.c) Structure and mass ratio of 3d, 6d, and -estradiol used in sample 1 (left) and sample 2 (right).d) Comparison of absorption spectra of 3d and 6d, and light emission spectra of white room light and white LED.The overlap between the excitation and absorption spectra in the 420-480-nm (sky blue color) range indicates that visible light is excitable.e) Schematic explaining the preparation procedure and afterglow readout procedure for samples with a stacked structure of samples 1 and 2. f)-(i) Demonstration of conventional afterglow readout from the stacked sample in the dark by using ultraviolet excitation.(ii) Demonstration of white room light-activated afterglow readout with unaided eyes in the dark of the stacked sample.The intensity of white room light is 0.21 mW cm −2 at the position of the sample upon conversion of the number of photons in the white light at 532 nm.(iii) White LED light-activated bright afterglow readout with unaided eyes under the white room light of the stacked sample.The intensity of white light excitation from the LED is 11.25 mW cm −2 at the sample position of the number of photons in the white light at 532 nm.The Intensity of white room light is 0.094 mW cm −2 at the position of the sample upon conversion of the number of photons in the white light at 532 nm.

Table 2 .
Summary of photophysical parameters related to triplet states.